Problem: Express this quotient in scientific notation: ${\frac{1.640\times 10^{0}} {2.0\times 10^{2}}}$
Solution: Start by collecting like terms together. $= {\frac{1.640} {2.0}} \times{\frac{10^{0}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.82 \times 10^{0\,-\,2}$ $= 0.82 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.82$ is the same as $8.20 \div 10$ , or $8.20 \times 10^{-1}$ $ = {8.20 \times 10^{-1}} \times 10^{-2} $ $= 8.20\times 10^{-3}$